Dynamical complexity driven by water temperature in a size-dependent phytoplankton–zooplankton model with environmental variability

Abstract

In this paper, we propose a stochastic phytoplankton–zooplankton (PZ) system modeling the growth dynamic of phytoplankton, where the death rate of zooplankton and the growth rate of phytoplankton are considered to be dependent on water temperature, and random environmental perturbation is characterized by mean-reverting Ornstein–Uhlenbeck process. Mathematical theoretical work mainly studies the stability, persistence, and Hopf bifurcation of deterministic PZ model, as well as analyzes the stochastic extinction, persistence in mean, and ergodic stationary distribution of stochastic PZ model, which provides a theoretical basis for numerical simulations. Numerical simulation work mainly reveals that water temperature plays a crucial role in influencing the dynamic of size-dependent phytoplankton–zooplankton interactions, whether in deterministic or random environments. An important conclusion of this study is that the increase of water temperature is able to induce bubbling effect, however, the small phytoplankton cell size can weaken this bubbling effect, and the large phytoplankton cell size can strengthen this bubbling effect, which supports the experimental conclusion that body size plays a key role in mitigating the negative impact of warming on predator–prey interactions. Further, it is found that the plankton with large body size has the advantages of stable and sustainable survival in the cold environment, while the plankton with small body size has advantages of stable and sustainable survival in the warm environment. Therefore, it can be inferred that plankton will evolve into large body size in the cold environment, but they will evolve into small body size in the warm environment.